Taylor-Couette-Poiseuille Flow

Quantitative Visualization of Taylor-Couette-Poiseuille Flows with MRI+... 

Taylor-Couette-Poiseuille Flow 4.4.2.1 Fundamental Hydrodynamics... 

Fig. 4.4.2 The discrete data points represent Taylor-Couette-Poiseuille flow regimes observed with MRI for r = 0.5 [41]. The curved boundaries were obtained for r = 0.77 with optical techniques [38]. The two inserts show MRI spin-tagging FLASH images of the SHV and PTV hydrodynamic modes.

Fig. 4.4.3 Experimental set-up for the MRI investigation of Taylor-Couette-Poiseuille flow. The electrical motor driving the shaft, as well as the pump, are placed 7.3 m away from the scanner to avoid interference with the magnetic fringe field.

Fig. 4.4.5 Gradual blurring (staring on locations marked by arrow) of MRI spin-tagging spin-echo images of Taylor—Couette—Poiseuille flow as the axial flow is increased (from left to right). The images correspond to longitudinal sections of the flow and the axial flow is upwards. The dashed line marks the location of one of the stationary helical vortices which characterize the SHV mode. This flow regime corresponds to the transition from the SHV (steady) to partial PTV (unsteady) regimes as Re increases, as shown in Figure 4.4.2.

Particle Dispersion in Oscillatory Taylor-Couette-Poiseuille Flow... 

Zhu, X., Campero, R.J., and Vigil, R.D., Axial mass transport in liquid-liquid Taylor-Couette-Poiseuille flow, Chem. Eng. Set, 55, 5079-5087, 2000. 

Jeng, T-M., Tzeng, S-C. and Lin, C-H. (2007). Heat transfer enhancement of Taylor-Couette-Poiseuille flow in an annulus by mounting longitudinal ribs on the rotating inner cylinder. International Journal of Heat and Mass Transfer, Vol. 50, No. 1-2, pp. 381-390. Lockerby, D.A., Reese, J.M., Emerson, D.R. and Barber, R.W. (2004). Velocity boundary condition at solid wall in rarefied gas calculations. Phys. Rev. E., 3rd Series, Vol. 70, No. 1, Paper 017303, July. 

MRI has been used as a non-invasive quantitative visualization technique to investigate a class of complex Taylor-Couette-Poiseuille (TCP) flows, which constitute a prototype of many mixing or fractionation processes. Here we focused on the vicinity of the Stationary Helical Vortex (SHV) regime characterized by a... 

Giordano, R.L.C., Giordano, R.C. and Cooney, C.L. (2000). Performance of a continuous Taylor-Couette-Poiseuille vortex flow enzymic reactor with suspended particles. Process Biochemistry, Vol. 35, No. 10, pp. 1093-1101. 

An important problem is to analyze the stability of fluid flows. With the exception of the Taylor-Couette and Saffman Taylor problems, this chapter has focused on stability questions when the base state of the system was one with no motion (or rigid-body motion), so that instability addresses the conditions for spontaneous onset of flow. An equally valid question is whether a particular flow, such as Poiseuille flow in a pipe (or any of the other flows that we have analyzed in previous chapters of this book), is stable, especially to infinitesimal perturbations as linear instability determines whether the particular flow is actually realizable in experiments. This question was first mentioned back in Chapter 3 when we analyzed simple unidirectional flow problems and noted that solutions such as Poiseuille s solution for flow through a tube was a valid solution of the Navier-Stokes equations for all Reynolds numbers, even though common experience tells us that beyond some critical Reynolds number there is a transition to turbulent flow in the tube. 

Couette flow is a laminar circular flow occurring between a rotating (inner) cylinder and a static one, and the extension via increased speed of rotation to centrifugally-driven instabilities leads to laminar Taylor vortex flow, tending to turbulent flow as speed increases. Poiseuille flow is axial. 

---